Recent progresses in viscous hydrodynamics and the shear viscosity of QGP

1. Recent progresses in viscous hydrodynamics and the shear viscosity of QGP • Motivation • Relativistic hydrodynamics • Results from viscous hydrodynamics • Conclusion & Outlook Victor Roy National Institute of Science Education and Research Bhubaneswar

2. Motivation of this talk Evaluate transport coefficient of QGP From first principle lattice QCD From phenomenological study Uncertain Viscous hydrodynamics & Transport model topic of this talk Nakamura et al. PRL 94,072305

3. Evolution of Heavy ion collision Hydrodynamic regime Assumption: Near local thermal equilibrium

4. Relativistic hydrodynamics EoS, Initial condition • Relaxation equation for shear and bulk stress Roy et al. PRC 85,024909

5. Input Parameters to viscous hydrodynamics EoS: Lattice+Hadron Resonance Gas Tc=175 MeV Borsanyi et al JHEP 11(2010)077 • and z are input in viscous hydrodynamics

6. Initial energy density & freeze-out Pb-Pb for 0-5% centrality at 2.76 TeV Glauber Model: Color Glass Condensate Model: Optical Glauber model V Roy et al Phys. Lett. B. 703, 313-317 (2011). Luzum et al. PRC 78, 034915 Cooper-Frey freeze-out:

7. 2+1D viscous hydrodynamics “AZHYDRO-KOLKATA” Initial condition: Glauber: Smooth CGC : Smooth (fKLN) QGP phase: Evolution: 2+1 D viscous hydrodynamics h/s: constant Hadronic Phase: Evolution: 2+1D viscous hydrodynamics h/s: constant Freeze-out: Hyper-surface: Smooth Viscous correction: Grad 14-moment Roy et al., PRC 86, 014902 LQCD EoS & HRG

8. Charged hadrons V2 ,Au-Au@200 GeV, RHIC Glauber CGC h/s value increases with centrality Larger h/s for CGC Roy et al. PRC 86,014902 (2012)

9. Charged hadrons V2 ,Pb-Pb@2.76 TeV, LHC Glauber CGC Roy et al, arXiv 1210.1700 h/s value increases with centrality Larger h/s for CGC

10. 2+1D viscous hydrodynamics + URQMD “VISHNU” Song et al., PRL106,192301(2011) Initial condition: Glauber: fluctuating CGC : fluctuating (MC-KLN) QGP phase: Evolution: 2+1 D viscous hydrodynamics h/s: constant Hadronic Phase: Evolution: Transport model URQMD h/s: temperature dependent Freeze-out: Hyper-surface: Non-smooth Viscous correction: Grad 14 moment LQCD EoS & HRG

11. Inclusion of viscosity in hadronic phase • High shear viscosity in late hadronic phase H song et al., PRL106,192301(2011) Value of extracted h/s depends on initial condition

12. 2+1D viscous hydrodynamics with h/s (T) Niemi et al., PRL106,212302 (2011) PRC 86,014909 (2012) Initial condition: Glauber: smooth QGP phase: Evolution: 2+1 D viscous hydrodynamics h/s: temperature dependent Hadronic Phase: Evolution: 2+1D viscous hydrodynamics, chemical freeze-out h/s: temperature dependent Freeze-out: Hyper-surface: Smooth Viscous correction: Grad 14-moment LQCD EoS & HRG s95 p-PCE-v1, Houvinen et al.,NPA, 837,26(2010)

13. Temperature Dependent h/s Au-Au @200GeV Pb-Pb @2.76TeV Niemi et al. PRL106,212302 RHIC @ 200 GeV Temperature dependence of h/s in QGP phase has little effect on v2(pT) LHC @2.76 TeV Temperature dependence of h/s in hadronic phase has little effect on v2(pT)

14. 3+1D event by event viscous hydrodynamics “MUSIC” Schenke et al., PRC 85,024901 (2012) Initial condition: Glauber: fluctuating (MC-Glauber) QGP phase: Evolution: 3+1 D viscous hydrodynamics h/s: constant Hadronic Phase: Evolution:3+1 D viscous hydrodynamics h/s: constant Freeze-out: Hyper-surface: Non-smooth Viscous correction: Relaxation time approximation df dependence on momentum ‘p’ LQCD EoS & HRG S95 p-v1, Houvinen et al.,NPA, 837,26(2010)

15. Results from 3+1D hydro h/s=0.08 h/s=0.16 hs 3+1D No assumption on hs symmetry Allows to explain hs dependence of experimental data Higher h/s needed for larger rapidity Schenke et al. PRL 106,042301 (2011)

16. Result from 3+1D hydrodynamics with fluctuating initial condition 0 0.5 1 1.5 2 Higher harmonics more sensitive to h/s Schenke et al., arXiv:1209.6330 PRC 85,024901

17. Comprehensive Heavy Ion Model Evaluation and Reporting Algorithm (CHIMERA) Initial condition: Glauber: Average of fluctuating condition Pre-equilibrium flow QGP phase: Evolution: 2+1 D viscous hydrodynamics h/s: constant Hadronic Phase: Evolution: Transport (URQMD) h/s: Temperature dependent Freeze-out: Hyper-surface: Smooth Viscous correction: Pratt, Torrieri formalism S Pratt et al., arXiv: 1208.0897 LQCD EoS & HRG Laine et al., PRD 73 (2006) Pratt et al., PRC 82 (2010)

18. Combined c2 analysis S Pratt et al., arXiv: 1208.0897 Initial energy density scales with Ncoll Initial energy density scales with Npart No pre equil flow Pre equil flow No pre equil flow Pre equil flow Experimental data: PHENIX (PRC 69, 034909) and STAR (PRL 92, 112301) p- Spectra + v2 + HBT radii in 0-20% centrality Au-Au collision at 200 GeV 0 < h/s < 6 x 1/4p

19. Conclusion & Outlook Au-Au @ 200 GeV Pb-Pb @ 2.76 TeV 1/4p < h/s < 6(1/4p) 1/4p < h/s < 4(1/4p) • Bulk Viscosity & Grad 14-moment correction to freeze-out distribution function • Large initial angular momentum of the reaction zone in non-central collisions

20. Thank You